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Home/Chain Registry/Block #2,286,453

Block #2,286,453

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 9/7/2017, 2:12:22 PM Β· Difficulty 10.9553 Β· 4,546,843 confirmations

TWN
Bi-Twin Chain

Interleaved pairs of primes that differ by 2, forming twin prime pairs at each level.

Block Header
Block Hash
3f9310efc41c0ab262d03f6ce070b9da82e959b9542fe8f1ed93eec89264e6fd
View on Chainz β†—

Difficulty

10.955326

Transactions

1

Size

200 B

Version

2

Bits

0af4903b

Nonce

66,805,634

Timestamp

9/7/2017, 2:12:22 PM

Confirmations

4,546,843

Merkle Root

40fcc4e8b5d40de46574264e8aa3e8befbbad11c1caac6c3903aca9cc2c98708
Transactions (1)
Coinbase40fcc4e8b5d40d…3aca9cc2c98708
1 in β†’ 1 out8.3200 XPM110 B
AZqGNmU1…G4Uirvho
Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) β€” it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

4.491 Γ— 10⁹⁴(95-digit number)
44915543637869714228…32215293143356205760
Discovered Prime Numbers
Lower: 2^k Γ— origin βˆ’ 1 | Upper: 2^k Γ— origin + 1

These are the actual prime numbers discovered by this block, computed using the verified Primecoin formula. Each number has been independently confirmed to pass the Fermat primality test. Use the FactorDB links to verify any number independently.

Level 0 β€” Twin Prime Pair (origin Β± 1)
origin βˆ’ 1
4.491 Γ— 10⁹⁴(95-digit number)
44915543637869714228…32215293143356205759
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
4.491 Γ— 10⁹⁴(95-digit number)
44915543637869714228…32215293143356205761
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: origin + 1 βˆ’ origin βˆ’ 1 = 2 (twin primes βœ“)
Level 1 β€” Twin Prime Pair (2^1 Γ— origin Β± 1)
2^1 Γ— origin βˆ’ 1
8.983 Γ— 10⁹⁴(95-digit number)
89831087275739428456…64430586286712411519
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
8.983 Γ— 10⁹⁴(95-digit number)
89831087275739428456…64430586286712411521
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^1 Γ— origin + 1 βˆ’ 2^1 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 2 β€” Twin Prime Pair (2^2 Γ— origin Β± 1)
2^2 Γ— origin βˆ’ 1
1.796 Γ— 10⁹⁡(96-digit number)
17966217455147885691…28861172573424823039
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.796 Γ— 10⁹⁡(96-digit number)
17966217455147885691…28861172573424823041
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^2 Γ— origin + 1 βˆ’ 2^2 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 3 β€” Twin Prime Pair (2^3 Γ— origin Β± 1)
2^3 Γ— origin βˆ’ 1
3.593 Γ— 10⁹⁡(96-digit number)
35932434910295771382…57722345146849646079
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
3.593 Γ— 10⁹⁡(96-digit number)
35932434910295771382…57722345146849646081
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^3 Γ— origin + 1 βˆ’ 2^3 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 4 β€” Twin Prime Pair (2^4 Γ— origin Β± 1)
2^4 Γ— origin βˆ’ 1
7.186 Γ— 10⁹⁡(96-digit number)
71864869820591542764…15444690293699292159
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
7.186 Γ— 10⁹⁡(96-digit number)
71864869820591542764…15444690293699292161
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)

What this block proved

The miner who found this block proved the existence of 10 consecutive prime numbers forming a Bi-Twin Chain. The prime chain origin β€” the large number shown above β€” anchors the chain and is divisible by a primorial (the product of small primes), cryptographically tying these prime numbers to this specific block.

View full Prime Chain Discovery page β†’
β˜…β˜…β˜†β˜†β˜†
Rarity
UncommonChain length 10
How Primecoin's Proof-of-Work Constructs These Primes

Primecoin stores a value called the prime chain origin in each block. The miner found a large integer such that when divided by a primorial (the product of small primes: 2 Γ— 3 Γ— 5 Γ— 7 Γ— …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial β€” that divisibility is part of the proof.

Prime Chain Origin = First Prime Γ— Primorial (2Β·3Β·5Β·7Β·11·…)
Source: Primecoin prime.cpp β€” CheckPrimeProofOfWork()

This is why the origin has many small prime factors β€” those factors are the primorial divisor. The chain then extends from the first prime using the TWN formula:

TWN: twin pairs (p, p+2) where p = origin/primorial βˆ’ 1 and p+2 = origin/primorial + 1
Verify on a Primecoin Node

Anyone running a Primecoin node can independently verify this block using the following RPC commands. Run these from the primecoin-cli command line or via the debug console in the Primecoin wallet.

1. Get block hash by height
getblockhash 2286453

Returns the block hash for a given block height. Use this to confirm the hash shown above matches the chain.

2. Get full block data
getblock 3f9310efc41c0ab262d03f6ce070b9da82e959b9542fe8f1ed93eec89264e6fd

Returns the full block header including difficulty, prime chain origin, prime chain type, transaction IDs, and all other fields shown on this page.

How to run these commands: To verify this data independently, open a terminal on your own Primecoin node and run primecoin-cli <command>. Alternatively, open the Primecoin-Qt wallet, go to Help β†’ Debug Window β†’ Console, and type the command directly. The node must be fully synced to this block height for the commands to return results.

Cross-reference on Chainz Explorer

Chainz is an independent Primecoin block explorer. Compare this block's data to verify accuracy.

View Block #2,286,453 on Chainz β†—
Circulating Supply:57,910,556 XPMΒ·at block #6,833,295 Β· updates every 60s
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